5.48 Work hours and education: The General Social Survey collects data on demogr

Question

5.48 Work hours and education: The General Social Survey collects data on demographics, education, and work, among many other characteristics of US residents. Using ANOVA, we can consider educational attainment levels for all 1,172 respondents at once. Below are the distributions of hours worked by educational attainment and relevant summary statistics that will be helpful in carrying out t his analysis. Educational attainment Less than HS (1) HS (2) Jr Col (3) Bachelor's (4) Graduate (5) Total 40.85 40.45 15.51 15.17 155 1172 Mcan SD 39.6 15.814.97 546 41.39 18.1 42.55 13.62 253 38.67 121 80 60 40 20 ,, Less than HS HS Jr Coll Graduate (a) Write hypotheses for evaluating whether the average number of hours worked varies across the five groups. Ha: At least one of the means is different Ha: At least one of the means is different Ha: At least one pair of means is the same

Explanation / Answer

n = Total number of respondents = 1172

number of groups ( Educantion attainment ) = 5

a ) In Anova

we test the hypothesis that

Ho : All the groups having same mean

against

H1 : Atleast one of the mean is different.

Here number of groups = 5

Correct option

A: Ho .mu1=mu2=mu3=mu4=m5

Ha : At least of the mean is different.

b) Anova table

i) D.F.

The number of groups =5

D.F. for groups =5-1 = 4

The total number of respondent = 1172

D.F. for total =1172-1 =1171

D.F. for residual = 1171 - 4 = 1167

ii) S.S.

Since M.S.S. = S.S / D.F

S.S. for degree = 4 * 501.54 = 2006.16

S.S. for total = S.S. for residual + S.S . for degree = 2006.16 + 267382 = 269388.16

iii) M.S.S.

M.S.S. = S.S /D.F

M.S.S. for residuals = S.S. for residuals / D.F. = 267382/ 1167 = 229.1191

iv) F-value = M.S. for degree / M.S. for residuals = 501.54 / 222.1191 = 2.1889

c) Value of test statistics =F-value =2.188

d) p-value= P(>F) = 0.0682

e) alpha =level of significance =0.05

Since p-value > alpha

Interpretation :

Since p>= alpha we accept the null hypothesis that all groups work the same average number of hours per week.

D.F S.S M.S.S F-value Pr(>F) degree (Groups) 4 2006.16 501.54 2.1889 0.0682 reisduals (error) 1167 267382 222.1191 ------------- Total 1171 269388.16 --------- -------------

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